Closed-loop pole: Difference between revisions

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In'''Closed-loop [[control theory]] therepoles''' are twothe main methodspositions of analyzingthe feedbackpoles systems: the(or [[transfer functioneigenvalues]]) (orof frequencya ___domain)closed-loop methodtransfer andfunction in the [[states-plane]]. space (controls)|stateThe space[[open-loop]] method.transfer function Whenis theequal transferto functionthe methodproduct isof used,all attentiontransfer isfunction focusedblocks onin the locations[[forward path]] in the [[s-planeblock diagram]]. where theThe closed-loop transfer function becomesis infiniteobtained by dividing (the '''poles''')open-loop ortransfer zerofunction by (the '''zeroes''').sum of Twoone different(1) transferand functionsthe areproduct of interestall totransfer thefunction designer.blocks Ifthroughout the [[feedback loopsloop]]. in theThe systemclosed-loop aretransfer openedfunction (thatmay isalso preventedbe fromobtained operating)by onealgebraic speaksor ofblock diagram manipulation. Once the '''openclosed-loop transfer function''', whileis ifobtained for the feedbacksystem, loopsthe areclosed-loop operatingpoles normallyare oneobtained speaksby ofsolving the '''closed-loop transfer[[characteristic function'''equation]]. ForThe characteristic equation is nothing more onthan setting the relationshipdenominator betweenof the twoclosed-loop seetransfer [[root-locus]]function to zero (0).

'''Closed-loopIn poles'''[[control theory]] there are thetwo positionsmain methods of theanalyzing polesfeedback (orsystems: the [[eigenvaluestransfer function]]) of(or afrequency closed-loop___domain) transfermethod function inand the [[s-plane]].state space The(controls)|state [[open-loopspace]] transfermethod. function isWhen equalthe totransfer thefunction productmethod ofis allused, transferattention functionis blocksfocused inon the [[forward path]]locations in the [[block diagrams-plane]]. where The closed-loopthe transfer function isbecomes obtained by dividinginfinite (the open-loop'''poles''') transferor function byzero (the sum'''zeroes'''). of oneTwo (1)different andtransfer thefunctions productare of allinterest transferto functionthe blocksdesigner. throughout If the [[feedback loop]].loops in Thethe closed-loopsystem transferare functionopened may(that alsois beprevented obtainedfrom byoperating) algebraicone orspeaks block diagram manipulation. Onceof the closed'''open-loop transfer function''', iswhile obtained forif the system,feedback theloops closed-loopare polesoperating arenormally obtainedone byspeaks solvingof the [[characteristic'''closed-loop transfer equation]]function'''. The characteristic equation is nothingFor more than settingon the denominatorrelationship ofbetween the closed-looptwo transfersee function to zero (0)[[root-locus]].

== Closed-loop poles in control theory ==